Redistribution of Parts in a Distribution Network

ABSTRACT

Redistributing parts includes defining locations. An actual inventory of parts is established among the locations, and a desired allocation of the parts is established among the locations. A demand for the parts at each location is determined using the actual inventory and the desired allocation. Paths are determined, where a path transfers an excess part from one location to another location. A transfer function describing a cost of transferring the excess part along the paths is generated. The transfer function is optimized to achieve the desired allocation of the excess parts at a minimum cost.

1. CLAIM OF PRIORITY

This application is a continuation of U.S. patent application Ser. No.11/696,297, filed on 4 Apr. 2007 and entitled “REDISTRIBUTION OF PARTSIN A DISTRIBUTION NETWORK” which is a divisional of U.S. patentapplication Ser. No. 10/033,103, filed on 25 Oct. 2001 and entitled“REDISTRIBUTION OF PARTS IN A DISTRIBUTION NETWORK”, now U.S. Pat. No.7,210,624 which claims the benefit of U.S. Provisional Application Ser.No. 60/243,659 filed 26 Oct. 2000 and entitled “SYSTEM AND METHOD FOROPTIMIZED DEPLOYMENT OF INVENTORY, OR RE-DISTRIBUTION OF EXISTINGINVENTORY, ACROSS A MULTI-ECHELON DISTRIBUTION NETWORK”. U.S. patentapplication Ser. No. 11/696,297, U.S. Pat. No. 7,210,624, and U.S.Provisional Application Ser. No. 60/243,659 are commonly assigned to theassignee of the present application. The disclosure of related U.S.patent application Ser. No. 11/696,297, U.S. Pat. No. 7,210,624, U.S.Provisional Application Ser. No. 60/243,659 are hereby incorporated byreference into the present disclosure as if fully set forth herein.

BACKGROUND

1. Technical Field of the Invention

This invention relates generally to the field of inventory distributionnetworks and more specifically to redistribution of parts in adistribution network.

2. Background of the Invention

Distribution networks may include one or more locations that receiveparts from a vendor and distribute the parts within the distributionnetwork in order to provide a customer with a product. The parts may be,for example, manufactured into a product within the distributionnetwork. Distribution networks may include locations that both supplyparts to and receive parts from other locations. Performance at eachlocation is thus affected by the performance at its suppliers. As aresult, maintaining an optimal inventory of parts at each location thatbest serves the customer while minimizing inventory costs poses achallenge for inventory managers.

SUMMARY OF THE INVENTION

In accordance with the present invention, disadvantages and problemsassociated with inventory deployment and redistribution techniques arereduced or eliminated.

According to one embodiment of the present invention, redistributingparts includes defining locations. An actual inventory of parts isestablished among the locations, and a desired allocation of the partsis established among the locations. A demand for the parts at eachlocation is determined using the actual inventory and the desiredallocation. Paths are determined, where a path transfers an excess partfrom one location to another location. A transfer function describing acost of transferring the excess part along the paths is generated. Thetransfer function is optimized to achieve the desired allocation of theexcess parts at a minimum cost.

Certain embodiments of the invention may provide one or more technicaladvantages. The present invention may be used to determine an optimizedinventory deployment plan that describes the inventory at each locationof a distribution network. The inventory deployment plan may optimizethe ability of the distribution network to satisfy customer demand whileconforming to business constraints. The inventory deployment plan maymaximize the ability of each location to fill an order, which may becalculated by minimizing total expected backorders for the network. Thepresent invention may be used to formulate a coverage function that isoptimized to determine an optimized deployment of the excess inventoryat the excess locations in the network to deficit locations. Thecoverage function describes the expected ability of each location tocompletely or partially fill a demand for a part, which may provide animproved measure of customer satisfaction.

The present invention may be used to calculate a demand for a part at alocation that accounts for a dependent demand and an independent demand.A dependent demand at a location describes the parts that the locationsupplies to other locations, and an independent demand at a locationdescribes the parts used at the location. Incorporating the independentand dependent demand into the demand may provide for a more accuratecalculation of the demand. The present invention may be used tocalculate a demand for a part at a location that takes into account theprobability that the part is repaired and placed back into the inventoryat the location. By taking into account repaired parts, the calculationof the demand may be more accurate.

The present invention may be used to calculate the availability of apart at a demand location that receives the part from multiple supplylocations. The demand location may order a certain proportion of partsfrom the supply locations in a particular order. The availability takesinto account the probability that a supply location supplies a part,given that no other supply location has supplied the part, which mayprovide a more realistic calculation of availability.

The present invention may be used to restrict the optimization usingconstraints. Constraints may include, a space limitation at a locationand a prohibition on new part purchases, the exclusion of a locationfrom distributing its excess inventory. The present invention may beused to provide an optimized redistribution of inventory among thelocations of a distribution network. Inventory of a part may beredistributed if there are excess inventory of this part at somelocations and deficit at other locations. The redistribution may beoptimized to lower costs associated with transferring parts from onelocation to another location.

Other technical advantages may be readily apparent to one skilled in theart from the figures, descriptions and claims included herein.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding of the present invention and itsfeatures and advantages, reference is now made to the followingdescription, taken in conjunction with the accompanying drawings, inwhich:

FIG. 1 illustrates an example distribution network for deploying andredistributing inventory of one or more parts among one or morelocations;

FIG. 2 illustrates an example system that generates optimized inventorydeployment and redistribution plans;

FIG. 3 illustrates an example method for deploying and redistributinginventory of one or more parts among one or more locations;

FIG. 4 illustrates an example method for calculating a demand for one ormore parts at one or more locations;

FIG. 5 illustrates an example method for estimating the availability ofone or more parts at one or more locations;

FIG. 6 illustrates an example method for formulating a coverage functionfor one or more parts at one or more locations; and

FIG. 7 illustrates an example method for redeploying a part among one ormore locations.

DETAILED DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates an example distribution network 20 for deploying andredistributing inventory of one or more parts among one or morelocations 22. Distribution network 20 includes locations 22 thatdistribute parts throughout distribution network 20. A part maycomprise, for example, a product, a portion of a product, a device usedto manufacture a product, or any other suitable item that may bedistributed from one location 22 to another location 22 in distributionnetwork 20.

In one embodiment, locations 22 include a central location 22 a and oneor more warehouse locations 22 b-d. Although central location 22 a andwarehouse locations 22 b-d are illustrated, distribution network 20 mayinclude any suitable number of central locations 22 and warehouselocations 22. Each location 22 may comprise a supply location and/or ademand location. A supply location supplies a part to a demand location,and may supply the part in response to an order for the part sent fromthe demand location. For example, warehouse location 22 b supplies partsto warehouse location 22 d. For example, warehouse locations 22 b-csupply parts to location 22 d. A location 22 may comprise both a demandlocation and a supply location. For example, warehouse location 22 breceives parts from central location 22 a and supplies parts towarehouse location 22 d. A supply endpoint such as central location 22 areceives parts from one or more external suppliers 24, for example, avendor, and distributes the parts to warehouse locations 22 b-d. Ademand endpoint such as warehouse location 22 d provides parts to one ormore external demands 32, for example, a customer.

Warehouse locations 22 b-d may include supply operations 26 b-d and/orrepair operations 28 b-d. A supply operation 26 sends an order for apart to a supply location, which in response sends the part to supplyoperation 26. A repair operation 28 may receive a broken part fromsupply operation 26 and send the broken part to a repair center 30.Repair center 30 repairs the part and sends the repaired part to, forexample, central location 22 a or back to supply operation 26 b.Alternatively, repair operation 28 d may receive a broken part fromsupply operation 26 d, repair the part, and send the repaired part backto supply operation 26 d.

The inventory for each part at each location 22 is monitored,continuously or periodically. In response to the inventory falling belowa predetermined level, an order is placed to bring the inventoryposition back up to a target level such as an optimized inventory level.A method for deploying inventory of one or more parts among one or morelocations to achieve optimized inventory levels is described in moredetail with reference to FIG. 2.

FIG. 2 illustrates an example system 34 that generates optimizedinventory deployment and redistribution plans. The inventory deploymentplan describes a distribution of parts among locations 22 ofdistribution network 20, and an inventory redistribution plan describesa manner of transferring inventory of parts from the excess locations tothe deficit locations to satisfy the inventory deployment plan.

System 34 may include a computer system 35, a server 36, and a database37, which may share data storage, communications, or other resourcesaccording to particular needs. Computer system 35 may includeappropriate input devices, output devices, mass storage media,processors, memory, or other components for receiving, processing,storing, and communicating information according to the operation ofsystem 34. As used in this document, the term “computer” is intended toencompass a personal computer, workstation, network computer, wirelessdata port, wireless telephone, personal digital assistant, one or moremicroprocessors within these or other devices, or any other suitableprocessing device.

Server 36 manages applications that generate optimized inventorydeployment and redistribution plans. Server 36 includes one or moresoftware components such as a preprocessing module 38 and a solver 39.Preprocessing module 38 may include a deployment module 40 and aredistribution module 41. Deployment module 40 may be used to generate acoverage function and constraints that describes the distribution ofparts among locations 22. Solver 39 optimizes the coverage function todetermine an optimized distribution of parts. Solver 39 may comprise amathematical programming solver such as CPLEX by ILOG, INC.Redistribution module 41 may be used to generate a transfer functionalong with the constraints that describes the transfer of parts amonglocations 22. Solver 39 optimizes the transfer function to determine acost optimal manner of redistributing parts.

Database 40 stores data that may be used by server 36. Data may include,for example, the history of the demand for each part at each location22, the lead time required to transport a part from one location 22 toanother location 22, and the maximum space capacity for a location 22.Computing system 35 and database 40 may be coupled to server 36 usingone or more local area networks (LANs), metropolitan area networks(MANs), wide area networks (WANs), a global computer network such as theInternet, or any other appropriate wired, optical, wireless, or otherlinks.

FIG. 3 illustrates an example method for deploying inventory of one ormore parts among one or more locations 22. Processing module 38initiates the method at step 46 by defining a number 1, 2, . . . , i, .. . , I of parts and a number 1, 2, . . . , j, . . . , J of locations22. For example, j=I, 2, 3, 4 refer to warehouse locations 22 a-d,respectively. At step 48, data is accessed from database 37. Data mayinclude, for example, a demand history of each part at each location 22.The demand history may describe the number of parts that each location22 requires. Data may include the repair history that may describe thecapability of each location 22 to repair a part. Data may include thelanes that may be used to transfer parts between locations 22, alongwith the costs associated with transporting parts along the lanes. Datamay include the cost of purchasing a part, the cost of holding a part inthe location as a percentage of the purchase cost for the part, and afixed cost associated with ordering a part.

At step 50, a demand for each part at each location 22 is calculated.The demand may include a dependent demand and an independent demand. Adependent demand at location 22 describes the parts that location 22supplies to other locations 22. An independent demand at location 22describes parts used at location 22. The demand at location 22 mayaccount for the probability that a part is repaired and placed back intothe inventory at location 22. Demand may be calculated by starting at ademand endpoint and ending at a supply endpoint of distribution network20. A method for calculating a demand for a part at each location 22 isdescribed in more detail with reference to FIG. 4.

A replenishment lead time for each part at each location 22 iscalculated at step 52. The replenishment lead time for a part atlocation 22 describes the time required for location 22 to receive thepart from another location 22. The replenishment lead time may becomputed by starting at a supply endpoint and ending at a demandendpoint. An availability lead-time for each part at each location 22 isestimated at step 54. The availability lead time at a location 22describes the waiting time due to back order at the location 22 plus thetransfer lead time from the supplier to location 22 and thereplenishment lead time for the supplier of location 22A method forestimating the availability lead time of a part at a location isdescribed in more detail with reference to FIG. 5.

A coverage function is formulated at step 56. The coverage functiondescribes the expected ability of a location 22 to completely orpartially fill an order for a part, and may be determined from thedemand, availability lead time of the part and the inventory level forthe part at location 22. The coverage function may be described usingthe expected backorder of the part at location 22. A method fordetermining the coverage is described in more detail with reference toFIG. 6.

The required inventory to satisfy the demand for the part at location 22at hundred percent is computed. The excess inventory of part isdetermined using the required amount and the actual inventory of part atthe location 22. Redistribution of the part inventory may not berequired if, for example, all locations 22 have at least sufficientamount to satisfy all demands for the part. If redistribution is notrequired for any part, deployment module 40 proceeds to step 63 toreport on any possible excess and the recommendation of no transfer forthe part. If redistribution is required, solver 39 optimizes thecoverage function at step 58. Optimizing the overall coverage functionmay be accomplished by minimizing the sum of expected backorders. Atstep 60, an optimized inventory level for each part at each location 22is determined. At step 63 the deployment solver 39 reports the optimizedinventory level for each part at each location 22.

At step 62, redistribution module 41 determines the supply and demandfor each part at each location from the actual inventory and the optimaldeployment. Redistribution module 41 proceeds to step 66 where thetransfer function describing the total cost related to transfer of partsbetween locations 22 is optimized. Minimizing the total cost associatedwith transporting the parts may optimize the transfer function. A methodfor determining optimized transfer plans for the parts between locations22 is described in more detail with reference to FIG. 7. At step 70, theoptimized transfer plans, the resulting inventory levels, and possibleexcess inventory of parts in the network are reported. After reportingthe result, the method is terminated.

FIG. 4 illustrates an example method for calculating a demand for one ormore parts at one or more locations 22. Deployment module 40 initiatesthe method at step 80 by selecting a part i. A location j is selected atstep 82. Location j may be selected such that the demand at a demandendpoint is calculated first, and the demand at a supply endpoint iscalculated last.

At step 84, an independent and the dependent demand for part i atlocation j is determined. The independent demand for part i at locationj may be represented by λ′_(ij). The dependent demands for part i atlocation j may be represented λ_(ik), for all k such that k is a demandpoint for location j. At step 86, the repair capability r_(ij) for parti at location j is determined. The repair capability r_(ij) may bedetermined from the proportion of demand for part i at location j thatis repairable at location j. Starting with demand end points j, thedemand λ_(ij) for part i is equal to its' independent demand. For anylocation that is not demand end point the demand λ_(ij) for part i iscalculated at step 88, and may be calculated using Equation (1):$\begin{matrix}{\lambda_{ij} = {\lambda_{ij}^{\prime} + {\sum\limits_{k\quad{is}\quad a\quad{demand}\quad{point}\quad{for}\quad j}{\left( {1 - r_{jk}} \right)\lambda_{ij}}}}} & (1)\end{matrix}$

At step 90, deployment module 40 determines if there is a next location.If there is no next location, deployment module 40 proceeds to step 92to determine whether there is a next part for which a demand is to bedetermined. If there is a next part, deployment module 40 returns tostep 80 to select the next part. If there is no next part, deploymentmodule 40 proceeds to step 94 to output the calculated demand for eachpart at each location. After outputting the demand, the method isterminated.

FIG. 5 illustrates an example method for estimating the availabilitylead-time of one or more parts at one or more locations 22. Deploymentmodule 40 initiates the method at step 102 by selecting a part i. Ademand location j is selected at step 104, and a supply location I_(k)is selected at step 106. The supply location I_(k) may be selected froma prioritized list of n supply locations I₁, . . . I_(n). For eachsupply location I_(k), the list may describe a proportion C_(iIkj) of ademand for part i at demand location j that is scheduled to be satisfiedby supply location i_(k), a probability α_(kj) that part i is filled atsupply location I_(k) for demand location j, and a lead time T_(iIkj)for a part i to flow from supply location I_(k) to demand location j.Demand location j and supply location i_(k) may be selected such thatthe availability lead-time at a supply endpoint is calculated first, andthe availability lead-time at a demand endpoint is calculated last.

At step 108, a probability Pi_(Ikj) of a supply location I_(k) fillingan order for part i placed by a demand location j, given that the orderis not filled by another supply location, is calculated. The probabilityP_(iIIj) supply location I_(I) may be computed using Equation (2):P_(\)=αC  (2)

At step 110, deployment module 40 determines whether there is a nextsupply location I_(k). If there is a next supply location, deploymentmodule 40 returns to step 106 to select the next supply location. Theprobability P_(ilkj) of the next supply location is filling an order forthe part placed by demand location j, given that the order is not filledby another supply location, may be computed at step 108 using theprocess described by the recursive Equations (3): $\begin{matrix}{{P_{{il}_{k}j} = {\alpha_{{il}_{k}j}C_{i_{kj}}}}{where}{C_{i_{l_{j}}}^{\prime} = C_{{ik}_{l}j}}{C_{{li}_{kj}}^{\prime} = {{C_{{li}_{k}j} + {\left( {1 - \alpha_{{il}_{k - 1}j}} \right)C_{{il}_{k - 1}j}\quad{for}\quad k}} > 1}}} & (3)\end{matrix}$

If there is no next supply location at step 110, deployment module 40proceeds to step 112 to output the probabilities of the supply locationsI_(k) fulfilling an order for part i placed by demand location j.

At step 113, an availability lead-time Ti_(j) for the part at eachlocation j is calculated. Availability lead-time Ti_(j) may becalculated according to the recursive Equation (4): $\begin{matrix}{T_{ij} = {\sum\limits_{k = 1}^{n}{\left( {T_{{il}_{k}j} + {\frac{{EBO}_{{il}_{k}}\left( S_{{il}_{k}} \right)}{\lambda_{{il}_{k}}}T_{{il}_{k}}}} \right)P_{{il}_{k}j}}}} & (4)\end{matrix}$

The expected number of back orders EBO (S_(ij)) having the inventorylevel S_(ij) of part i at location j may be defined using Equation (5):$\begin{matrix}{{EBO}_{ij} = {\sum\limits_{x = S_{ij}}^{\infty}{\left( {x - {\chi\quad S_{ij}}} \right){{P\left( X \middle| \mu_{ij} \right)}.}}}} & (5)\end{matrix}$

At step 114, the replenishment lead-time for part ∂_(ij) at demandlocation j is calculated. The replenishment lead-time _(ij) for part iat location j may be calculated using Equation (6):∂_(ij) =r _(ij)τ_(ij)+(1−r _(ij))T _(ij)  (6)

Where τ_(ij) represents the repair lead time for part i at demandlocation j,

The demand over lead-time or in pipeline value μ_(ij) of a part i atdemand location j is estimated at step 116. The demand over lead-time orin pipeline value may be estimated using Equation (7):μ_(ij)=λ_(ij)∂_(ij)  7)

At step 118, deployment module 40 determines whether there is a nextdemand location. If there is a next demand location, deployment module40 returns to step 104 to select the next demand location. If there isno next demand location, deployment module 40 proceeds to step 120 todetermine whether there is a next part. If there is a next part,deployment module 40 returns to step 102 to select the next part. Ifthere is no next part, deployment module 40 proceeds to step 122 toreport the lead-time demand of each part at each location 22. Afterreporting the lead-time demand, the method is terminated.

FIG. 6 illustrates an example method for generating a coverage functionfor one or more parts at one or more locations 22. Deployment module 40initiates the method at step 132 by selecting a location j. A part i isselected at step 134.

At step 136, a completely filled demand D_(c) for part i at location jis calculated at step 136. A completely filled demand D_(c) may bedescribed by Equation (8): $\begin{matrix}{D_{c} = {\sum\limits_{x = 0}^{S_{ij} - 1}{{xP}\left( X \middle| \mu_{ij} \right)}}} & (8)\end{matrix}$

where P(X|μ_(ij))=e^(−μ) ^(ij) μ_(ij) ^(x)x! is the Poisson probabilitymass function for the distribution of demand with mean μ_(ij). Apartially filled demand D_(p) for part i at location j is calculated atstep 138. The partially filled D_(p) demand may be described by Equation(9): $\begin{matrix}{D_{p} = {{\chi\left( {S_{ij} - 1} \right)}\left\lbrack {1 - {\sum\limits_{x = 0}^{S - 1}{P\left( X \middle| \mu_{ij} \right)}}} \right\rbrack}} & (9)\end{matrix}$

where χ is the percentage of partial fill allowed for the part. At step140, a coverage function for part i at location j is determined. Thecoverage function for part i at location j describes the expectedproportion of filled demand for part i at location j, and maybeexpressed using Equation (10): $\begin{matrix}{{\left\{ {{\sum\limits_{x = 0}^{S_{ij} - 1}{{xP}\left( X \middle| \mu_{ij} \right)}} + {\chi{\sum\limits_{x = S}^{\infty}{\left( {S_{ij} - 1} \right){P\left( X \middle| \mu_{ij} \right)}}}}} \right\}/\mu_{ij}} = {\left\{ {{\sum\limits_{x = 0}^{S_{ij} - 1}{\left( {x - {\chi\left( {S_{ij} - 1} \right)}} \right){P\left( X \middle| \mu_{ij} \right)}}} + {\chi\left( {S_{ij} - 1} \right)}} \right\}/\mu_{ij}}} & (10)\end{matrix}$

At step 142, deployment module 40 determines whether there is a nextpart. If there is a next part, deployment module 40 returns to step 134to select the next part. If there is no next part, deployment module 40proceeds to step 144 to determine whether there is a next location. Ifthere is a next location, deployment module 40 returns to step 132 toselect the next location. If there is no next location, deploymentmodule 40 proceeds to step 146 to determine the coverage function forthe number of parts at the number of locations. The coverage functionmay be expressed as the weighted average of coverage for the parts atlocations. The coverage function for the parts at the locations may beexpressed by the expression (11): $\begin{matrix}{\sum\limits_{j = 1}^{J}{\left\{ {\sum\limits_{i = 1}^{I}{\left( {\beta_{ij}/\mu_{ij}} \right)\left\lbrack {{\sum\limits_{x = 0}^{S_{ij}}{\left\lbrack {x - {\chi\quad S_{ij}}} \right\rbrack{P\left( X \middle| \mu_{ij} \right)}}} + {\chi\quad S_{ij}}} \right\rbrack}} \right\}/{\sum\limits_{i = 1}^{I}\mu_{ij}}}} & (11)\end{matrix}$

where β_(ij) represents a weight of part i, which may be based on animportance measure of part i. At step 148, constraints for the coveragefunction may be defined. Constraints may include, the following:

The total number of part i used is less than or equal to the totalinitial on hand inventory of part i, which may be expressed by Equation(12) $\begin{matrix}{{\sum\limits_{j = 1}^{J}S_{ij}} \leq {\sum\limits_{j = 1}^{J}{{IOH}_{i}{\forall i}}}} & (12)\end{matrix}$

The total volume occupied by parts at each location j is less than orequal to the volume capacity limit V_(j) at location j, which may beexpressed by Equation (13): $\begin{matrix}{{{\sum\limits_{i = 1}^{I}{v_{i}S_{ij}}} \leq V_{j}},{\forall j}} & (13)\end{matrix}$

and the stock levels S_(ij) are integers.

At step 150, the coverage function is converted to a Backorder function.Using the backorder function may provide for a simpler optimizationprocess. The backorder function may be expressed as in (14):$\begin{matrix}{\sum\limits_{j = 1}^{J}{\sum\limits_{i = 1}^{I}{{EBO}_{ij}\left( S_{ij} \right)}}} & (14)\end{matrix}$

Minimizing the expected backorder is equivalent to maximizing theexpected coverage. The constraints may be expressed by Equations (15):$\begin{matrix}{{{\sum\limits_{j = 1}^{J}S_{ij}} \leq {\sum\limits_{j = 1}^{J}{{IOH}_{i}\quad{\forall i}}}}{{{\sum\limits_{i = 1}^{I_{1}}{v_{i}S_{ij}}} \leq V_{j}},{\forall j}}{S_{ij}\quad{are}\quad{integers}}} & (15)\end{matrix}$

At step 154, the coverage function and constraints may be linearized inorder to allow the coverage function to be optimized by solver 39. Tolinearize the coverage function and constraints, the non-linear terms ofthe coverage function and constraints may be approximated by linearterms. The non-linear terms are discrete and convex, so a first-orderlinear approximation using the finite difference for two neighboringdiscontinuous points may be used to approximate each non-linear term.Each non-linear term in the coverage function and the constraints isreplaced with a continuous variable t, and a linearization constraintthat describes the under estimation at points of discontinuity is addedto the constraints.

The objective function that measures expected backorder as expressed byEquation (14), may be linearized according to expression (15):$\begin{matrix}{\sum\limits_{j = 1}^{J}{\sum\limits_{i = 1}^{I}{t_{ij}.}}} & (15)\end{matrix}$

The linearization constraint may be expressed by Equation (16):t _(ij) ≧m _(ij)(X−X _(ij))+b _(ij) ,∀S _(ij) <X _(ij) S _(upper,∀)_(i,j)  (16)

where m_(ij)=P(X>X_(ij)|μ_(ij)),b_(ij)=P(X>X_(ij)|μ_(ij)(X−X_(ij))+EBO_(ij)(X_(ij)+1), and S_(upper) isthe upper bound on the inventory for part i at location j. Otherconstraints may be expressed by Equations (37): $\begin{matrix}{{{\sum\limits_{j = 1}^{J}S_{ij}} \leq {\sum\limits_{j = 1}^{J}{{IOH}_{i}\quad{\forall i}}}}{{{\sum\limits_{i = 1}^{I_{1}}{v_{i}S_{ij}}} \leq V_{j}},{\forall j}}{{S_{ij}\quad{are}\quad{integers}},{{\forall i} = 1},\ldots\quad,I_{2},{\forall j}}} & (17)\end{matrix}$

After linearizing the coverage function, the method is terminated.

FIG. 7 illustrates an example method for redeploying a part among one ormore locations 22. Redistribution module 41 initiates the method at step170 by receiving from database 37 an actual inventory and an optimizedinventory for the part at each location 22. The optimized inventory maybe determined according to a method described with reference to FIG. 3.At step 172, a demand D_(j) for the part at each location j isdetermined. The demand for the part at location j may be computed fromthe difference between the optimized inventory for the part at locationj and the actual inventory for the part at location j. A positive demandD_(j) represents a demand or deficit for the part at that location,while a negative demand D_(j) represents a supply or excess for the partat that location.

A dummy location may be added to distribution network 20. The dummylocation may be defined as a location with a positive demand D_(j) equalto the difference between the total excess and the total demand. Thedummy node acts as a sink to attract left over excess of the part in thenetwork. A path set for each location j is established at step 174. Apath set for location j may be defined by Out(j), which lists the pathson which parts may be transported from location j to another location k.

A transition matrix that describes the paths between locations isinitialized at step 176. The transition matrix may be defined as, forexample, a J-by-J matrix T, where T[j,k] is true if location j isconnected by a path to location k, and it is false otherwise. Settingthe elements of T equal to false may initialize transition matrix T. Atstep 178, a location j is selected. Other locations k that are connectedto location j are determined at step 180. The following process may beused to determine locations k: Let LIST ={j}   While (LIST is not empty)    Remove an element m from LIST     Let T[j,m] = true     For k inOut(m)       If (T[j,k] ≠ true)         Add k to LIST       End if    End for   End while

At step 182, redistribution module 41 determines whether there is a nextlocation. If there is a next location, redistribution module 41 returnsto step 178 to select the next location. If there is no next location,redistribution module 41 proceeds to step 184 to output transitionmatrix T.

At step 186, a transfer cost C_(jk) associated with transferring thepart from location j to location k is determined for each path. Thepaths to the dummy location may be associated with an infinite transfercost. A transfer cost function is optimized by solver 39 at step 188.The transfer cost function for each part may be defined by Equation(18): $\begin{matrix}{\sum\limits_{j = 1}^{J}{\sum\limits_{k = 1}^{I}{C_{jk}X_{jk}}}} & (18)\end{matrix}$

where X_(jk) represents the number of the part transferred from locationj to location k. Constraints for the transfer cost function may include,constraints defined by Equations (41): $\begin{matrix}{{{{{\sum\limits_{j}X_{jk}} - {\sum\limits_{j}X_{kj}}} = D_{k}},{\forall k}}{X_{jk} \geq {0\quad{are}\quad{integers}}}} & (19)\end{matrix}$

Optimization of the transfer cost function results in a set of triplets(j,k,X_(jk)), where each triplet represents an optimal transfer. At step190, the optimal transfers are reported. After reporting the transfers,the method is terminated.

Certain embodiments of the invention may provide one or more technicaladvantages over previous inventory deployment and redistributiontechniques. The present invention may be used to determine an optimizeddeployment plan for the existing inventory in a distribution network 20.The inventory deployment plan may optimize the ability of distributionnetwork 20 to satisfy customer demand using only the existing inventorywhile conforming to business constraints. The inventory deployment planmay maximize the contribution of the part to the systems ability to fillan order, which may be calculated by minimizing overall expectedbackorder for the distribution network. The present invention may beused to formulate a coverage function that is optimized to determine anoptimized inventory deployment plan. The coverage function describes theexpected ability of each location 22 to completely or partially fill ademand for a part, which may provide an improved measure of customersatisfaction.

The present invention may be used to calculate a demand for a part at alocation 22 that accounts for a dependent demand and an independentdemand. A dependent demand at a location 22 describes the parts thatlocation 22 supplies to other locations 22, and an independent demand atlocation 22 describes the parts used at location 22. Incorporating theindependent and dependent demand into the demand may provide for a moreaccurate calculation of the demand. The present invention may be used tocalculate a demand for a part at a location 22 that takes into accountthe probability that the part is repaired and placed back into theinventory at location 22. By taking into account the repaired parts, thecalculation of the demand may be more accurate.

The present invention may be used to calculate the availability of apart at a demand location 22 that receives the part from multiple supplylocations 22. Demand location 22 may order a certain proportion of partsfrom supply locations 22 in a particular order. The availability takesinto account the probability that a supply location 22 supplies a part,given that no other supply location 22 has supplied the part, which mayprovide a more realistic calculation of availability.

The present invention may be used to restrict the optimization usingconstraints. Constraints may include the prohibition of new purchases,and a space limitation at each location 22. The present invention mayalso be used to determine an optimized inventory redistribution planthat provides a balance between the excess and deficit for a part amonglocations 22 of distributed network 20. Parts may be redistributed if anactual inventory does not meet an optimized inventory. Theredistribution may be optimized to lower costs associated withtransferring parts from one location 22 to another location 22.

Although an embodiment of the invention and its advantages are describedin detail, a person skilled in the art could make various alterations,additions, and omissions without departing from the spirit and scope ofthe present invention as defined by the appended claims.

1. A method for redistributing a plurality of parts, comprising:defining a plurality of locations; establishing an actual inventory of aplurality of parts among the locations; establishing a desiredallocation of the parts among the locations; determining a demand forthe parts at each location using the actual inventory and the desiredallocation; determining a plurality of paths, a path being operable totransfer an excess part from one location to another location;generating a transfer function describing a cost of transferring theexcess part along the paths; and optimizing the transfer function toachieve the desired allocation of the excess parts at a minimum cost. 2.The method of claim 1, wherein: the transfer function describes the costassociated with transferring a part along a plurality of alternativepaths; and optimizing the transfer function comprises minimizing thetransfer function.
 3. The method of claim 1, wherein determining thepaths comprises sending a notification if there is no path between onelocation and any of the other locations.
 4. The method of claim 1,wherein establishing the desired allocation comprises calculating anoptimized allocation of the excess parts among the locations.
 5. Themethod of claim 1, further comprising adding a dummy location with anassociated demand and an infinite transfer cost.
 6. The method of claim1, further comprising satisfying a constraint requiring that the partstransferred to a location and the parts transferred from the locationsatisfy the demand for the parts at the location.
 7. Logic embodied in acomputer-readable medium and when executed by a computer operable to:define a plurality of locations; establish an actual inventory of aplurality of parts among the locations; establish a desired allocationof the parts among the locations; determine a demand for the parts ateach location using the actual inventory and the desired allocation;determine a plurality of paths, a path being operable to transfer a partfrom one location to another location; generate a transfer functiondescribing transferring a plurality of excess parts along the paths; andoptimize the transfer function to achieve the desired allocation of theexcess parts at a minimum cost.
 8. The logic of claim 7, wherein: thetransfer function describes a cost associated with transferring theexcess parts along a plurality of alternative paths; and the logicfurther operable to optimize the transfer function by minimizing thetransfer function.
 9. The logic of claim 7, wherein the logic is furtheroperable to determine the paths by sending a notification if there is nopath between one location and another location.
 10. The logic of claim7, wherein the logic is further operable to establish the desireddistribution by calculating an optimized allocation of the excess partsamong the locations.
 11. The logic of claim 7, wherein the logic isfurther operable to add a dummy location with an associated demand andan infinite transfer cost.
 12. The logic of claim 7, wherein the logicis further operable to satisfy a constraint requiring that the partstransferred to a location and the parts transferred from the locationsatisfy the demand for the parts at the location.
 13. A method forredistributing a part, comprising: defining a plurality of locations;establishing an actual inventory of a plurality of parts among thelocations; establishing an optimized allocation of the parts among thelocations; determining a demand for a part at each location using theactual inventory and the optimized allocation; determining a pluralityof paths, a path being operable to transfer a part from one location toanother location; generating a transfer function cost being associatedwith transferring a part along a plurality of alternative paths;satisfying a constraint requiring that the parts transferred to alocation and the parts transferred from the location satisfy the demandfor the parts at the location; and minimizing the transfer function toachieve the desired allocation of a plurality of excess parts at aminimum cost.